What is the main difference between a torsion bar and a anti-roll bar in vehicles?

Both the Anti Roll Bar and Torsional Bar / Torsion beam work on the same principle - torsion or twisting of a beam to provide an elastic mechanical connection between opposite sides of a suspension.

I've differentiated between Anti Roll Bars and Torsion Beam Axles in the following sections

Anti-Roll Bar ( henceforth referred to as ARB )

As the name suggests, an ARB prevents excessive sideways tilting movement (Roll) of the vehicle while taking turns. The anti roll bar is usually a thin and shaped bar that connects two sides of an independent suspension system ( mostly used in the front wheels ) so that when one suspension moves up or down, the movement is PARTIALLY transferred to the other wheel too and thus helps maintain a mechanical connection with flexibility ( due to torsion ).

An ARB is also referred to as a Torsion bar sometimes. The ARB is attached by means ofpin joints or ball joints to the suspension linkages on either side and by means of bracket mounted pin-joints to the under body of the vehicle.

These linkages are a key difference between Anti Roll Bars and Torsion Beams. Torsion Beams are typically welded to the trailing arms of rear axles

Couple Torsion Beam Axle / Twist Beam Axle (henceforth referred to as CTBA )

A CTBA is a much thicker formed metal beam that is welded to a set of  trailing arms. The torsion beam acts as a flexible mechanical link ( similar to the anti roll bar ) with a high torsional stiffness compared to the anti-roll bar